Arnold Schwarzenegger fired back at Donald Trump's allegations that the actor and politician was fired from "The New Celebrity Apprentice."

In typical Donald Trump fashion, the president tweeted Saturday that his replacement at the "The New Celebrity Apprentice" reality television show is to blame for its poor ratings and not, as Schwarzenegger says, Trump's continued involvement with the show.

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But the "Terminator" star responded via Twitter, saying, "You should think about hiring a new joke writer and a fact checker."

Schwarzenegger, who replaced Trump as host of the show while the president remained its executive producer, announced Friday he's through. He said even if he were asked again, he wouldn't want to host the show.

"With Trump being involved in the show, people have a bad taste and don't want to participate as a spectator or as a sponsor or in any other way support the show," he said in an interview with the Empire website. "It's a very divisive period now, and I think this show got caught up in all that division."

But Trump, who has taunted Schwarzenegger for the show's poor performance in the ratings and even mocked him during an address at the National Prayer Breakfast, tweeted in response Saturday: "Arnold Schwarzenegger isn't voluntarily leaving the Apprentice, he was fired by his bad (pathetic) ratings, not by me. Sad end to great show."

The show wrapped up its 15th season last month. It averaged fewer than 5 million viewers per episode. That was lower than any other incarnation except for a 2010 Trump-hosted edition without celebrities, and the most poorly-rated edition among the youthful viewers NBC cares most about, the Nielsen company said.

NBC had no immediate comment about whether the show would return with a new host. The former California governor said he wouldn't mind working with NBC and producer Mark Burnett again "on a show that doesn't have this baggage."